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225  Faltings' Finiteness Dimension of Local Cohomology Modules Over Local CohenMacaulay Rings Bahmanpour, Kamal; Naghipour, Reza
Let $(R, \frak m)$ denote a local CohenMacaulay ring and $I$
a nonnilpotent ideal of $R$. The purpose of this article is
to investigate Faltings' finiteness
dimension $f_I(R)$ and equidimensionalness of certain homomorphic
image of $R$. As a consequence
we deduce that $f_I(R)=\operatorname{max}\{1, \operatorname{ht} I\}$
and if $\operatorname{mAss}_R(R/I)$
is contained in $\operatorname{Ass}_R(R)$, then the ring $R/ I+\cup_{n\geq
1}(0:_RI^n)$ is equidimensional of dimension $\dim R1$.
Moreover, we will obtain a lower bound for injective dimension
of the local cohomology module $H^{\operatorname{ht} I}_I(R)$, in the case
$(R, \frak m)$ is a complete equidimensional local ring.


235  Topology of Certain Quotient Spaces of Stiefel Manifolds Basu, Samik; Subhash, B
We compute the cohomology of the right generalised projective
Stiefel manifolds. Following this, we discuss some easy applications
of the computations to the ranks of complementary bundles, and
bounds on the span and immersibility.


246  On Radicals of Green's Relations in Ordered Semigroups Bhuniya, Anjan Kumar; Hansda, Kalyan
In this paper, we give a new definition of radicals of Green's
relations in an ordered semigroup and characterize left regular
(right regular), intra regular ordered semigroups by radicals
of Green's relations. Also we characterize the ordered semigroups
which are unions and complete semilattices of tsimple ordered
semigroups.


253  On a Yamabe Type Problem in Finsler Geometry Chen, Bin; Zhao, Lili
In this paper, a new notion of scalar curvature for a Finsler
metric $F$ is introduced, and two conformal invariants $Y(M,F)$
and $C(M,F)$ are defined. We prove that there exists a Finsler
metric with constant scalar curvature in the conformal class
of $F$ if the Cartan torsion of $F$ is sufficiently small and
$Y(M,F)C(M,F)\lt Y(\mathbb{S}^n)$ where $Y(\mathbb{S}^n)$ is the
Yamabe constant of the standard sphere.


269  Characterizations and Representations of Core and Dual Core Inverses Chen, Jianlong; Zhu, Huihui; Patricio, Pedro; Zhang, Yulin
In this
paper,
double commutativity and the reverse order law for the core inverse
are considered. Then, new characterizations of the MoorePenrose
inverse of a regular element are given by onesided invertibilities
in a ring. Furthermore, the characterizations and representations
of
the core and dual core inverses of a regular element are considered.


283  Twisted Alexander Invariants Detect Trivial Links Friedl, Stefan; Vidussi, Stefano
It follows from earlier work of SilverWilliams and the authors
that twisted Alexander polynomials detect the unknot and the
Hopf link.
We now show that twisted Alexander polynomials also detect the
trefoil and the figure8 knot,
that twisted Alexander polynomials detect whether a link is split
and that twisted Alexander modules detect trivial links. We use
this result to provide algorithms for detecting whether a link
is the unlink, whether it is split and whether it is totally
split.


300  Luzintype Holomorphic Approximation on Closed Subsets of Open Riemann Surfaces Gauthier, Paul M; Sharifi, Fatemeh
It is known that if $E$ is a closed subset of an open Riemann
surface $R$ and $f$ is a holomorphic function on a neighbourhood
of $E,$ then it is ``usually" not possible to approximate $f$
uniformly by functions holomorphic on all of $R.$ We show, however,
that for every open Riemann surface $R$ and every closed subset
$E\subset R,$ there is closed subset $F\subset E,$ which approximates
$E$ extremely well, such that every function holomorphic on $F$
can be approximated much better than uniformly by functions holomorphic
on $R$.


309  A Congruence Modulo Four for Real Schubert Calculus with Isotropic Flags Hein, Nickolas; Sottile, Frank; Zelenko, Igor
We previously obtained a congruence modulo four for the number
of real solutions to many Schubert problems on
a square Grassmannian given by osculating flags.
Here, we consider Schubert problems given by more general isotropic
flags, and prove this
congruence modulo four for the largest class of Schubert problems
that could be expected to exhibit this
congruence.


319  The Weakly Nilpotent Graph of a Commutative Ring Khojasteh, Sohiela; Nikmehr, Mohammad Javad
Let $R$ be a commutative ring with nonzero identity. In this
paper, we introduced the weakly nilpotent graph of a commutative
ring. The weakly nilpotent graph of $R$ is denoted by $\Gamma_w(R)$
is a graph with the vertex set $R^{*}$ and two vertices $x$ and
$y$ are adjacent if and only if $xy\in N(R)^{*}$, where $R^{*}=R\setminus\{0\}$
and $N(R)^{*}$ is the set of all nonzero nilpotent elements
of $R$. In this article, we determine the diameter of weakly
nilpotent graph of an Artinian ring. We prove that if $\Gamma_w(R)$
is a forest, then $\Gamma_w(R)$ is a union of a star and some
isolated vertices. We study the clique number, the chromatic
number and the independence number of $\Gamma_w(R)$. Among other
results, we show that for an Artinian ring $R$, $\Gamma_w(R)$
is not a disjoint union of cycles or a unicyclic graph. For Artinan
ring, we determine $\operatorname{diam}(\overline{\Gamma_w(R)})$. Finally, we
characterize all commutative rings $R$ for which $\overline{\Gamma_w(R)}$
is a cycle, where $\overline{\Gamma_w(R)}$ is the complement
of the weakly nilpotent graph of $R$.


329  Nonvanishing of Central Values of $L$functions of Newforms in $S_2 (\Gamma_0 (dp^2))$ Twisted by Quadratic Characters Le Fourn, Samuel
We prove that for $d \in \{ 2,3,5,7,13 \}$ and $K$ a quadratic
(or rational) field of discriminant $D$ and Dirichlet character
$\chi$, if a prime $p$ is large enough compared to $D$, there
is a newform $f \in S_2(\Gamma_0(dp^2))$ with sign $(+1)$ with
respect to the AtkinLehner involution $w_{p^2}$ such that $L(f
\otimes \chi,1) \neq 0$. This result is obtained through an estimate
of a weighted sum of twists of $L$functions which generalises
a result of Ellenberg. It relies on the approximate functional
equation for the $L$functions $L(f \otimes \chi, \cdot)$ and
a Petersson trace formula restricted to AtkinLehner eigenspaces.
An application of this nonvanishing theorem will be given in
terms of existence of rank zero quotients of some twisted jacobians,
which generalises a result of Darmon and Merel.


350  Isometry on Linear $n$Gquasi Normed Spaces Ma, Yumei
This paper generalizes the Aleksandrov problem: the MazurUlam
theorem on $n$Gquasi normed spaces. It proves that a one$n$distance
preserving mapping is an $n$isometry if and only if it has the
zero$n$Gquasi preserving property, and two kinds of $n$isometries
on $n$Gquasi normed space are equivalent; we generalize the
Benz theorem to nnormed spaces with no restrictions on the dimension
of spaces.


364  On the Roughness of Quasinilpotency Property of One–parameter Semigroups Preda, Ciprian
Let $\mathbf{S}:=\{S(t)\}_{t\geq0}$ be a C$_0$semigroup of quasinilpotent
operators
(i.e. $\sigma(S(t))=\{0\}$ for each $t\gt 0$).
In the dynamical systems theory the above quasinilpotency property
is equivalent
to a very strong concept of stability for the solutions of autonomous
systems.
This concept is frequently called superstability and weakens
the classical finite time extinction property
(roughly speaking, disappearing solutions).
We show that under some assumptions, the quasinilpotency, or
equivalently, the superstability property
of a C$_0$semigroup is preserved under the perturbations of
its infinitesimal generator.


372  Coaxer Lattices Rao, M. Sambasiva
The notion of coaxers is introduced in a pseudocomplemented
distributive lattice. Boolean algebras are characterized in terms
of coaxer ideals and congruences. The concept of coaxer lattices
is introduced in pseudocomplemented distributive lattices and
characterized in terms of coaxer ideals and maximal ideals. Finally,
the coaxer lattices are also characterized in topological terms.


381  The Bifurcation Diagram of Cubic Polynomial Vector Fields on $\mathbb{C}\mathbb{P}^1$ Rousseau, C.
In this paper we give the bifurcation diagram
of the family of cubic vector fields $\dot z=z^3+ \epsilon_1z+\epsilon_0$
for $z\in \mathbb{C}\mathbb{P}^1$, depending on the values of
$\epsilon_1,\epsilon_0\in\mathbb{C}$.
The bifurcation diagram is in $\mathbb{R}^4$, but its conic structure
allows describing it for parameter values in $\mathbb{S}^3$. There are
two open simply connected regions of structurally stable vector
fields separated by surfaces corresponding to bifurcations of
homoclinic connections between two separatrices of the pole at
infinity. These branch from the codimension 2 curve of double
singular points. We also explain the bifurcation of homoclinic
connection in terms of the description of Douady and Sentenac
of polynomial vector fields.


402  Invariant Means on a Class of von Neumann Algebras Related to Ultraspherical Hypergroups II Shravan Kumar, N.
Let $K$ be an ultraspherical hypergroup associated to a locally
compact group $G$ and a spherical projector $\pi$ and let $VN(K)$
denote the dual of the Fourier algebra $A(K)$ corresponding to
$K.$ In this note, we show that the set of invariant means on
$VN(K)$ is singleton if and only if $K$ is discrete. Here $K$
need not be second countable. We also study invariant means on
the dual of the Fourier algebra $A_0(K),$ the closure of $A(K)$
in the $cb$multiplier norm. Finally, we consider generalized
translations and generalized invariant means.


411  On Gibbs Measures and Spectra of Ruelle Transfer Operators Stoyanov, Luchezar
We prove a comprehensive version of the RuellePerronFrobenius
Theorem
with explicit estimates of the spectral radius of the Ruelle
transfer operator and various other
quantities related to spectral properties of this operator. The
novelty here is that the Hölder
constant of the function generating the operator appears only
polynomially, not exponentially as
in previous known estimates.


422  New Superquadratic Conditions for Asymptotically Periodic Schrödinger Equations Tang, Xianhua
This paper is dedicated to studying the
semilinear Schrödinger equation
$$
\left\{
\begin{array}{ll}
\triangle u+V(x)u=f(x, u), \ \ \ \ x\in {\mathbf{R}}^{N},
\\
u\in H^{1}({\mathbf{R}}^{N}),
\end{array}
\right.
$$
where $f$ is a superlinear, subcritical nonlinearity. It focuses
on the case where
$V(x)=V_0(x)+V_1(x)$, $V_0\in C(\mathbf{R}^N)$, $V_0(x)$ is 1periodic
in each of $x_1, x_2, \ldots, x_N$ and
$\sup[\sigma(\triangle +V_0)\cap (\infty, 0)]\lt 0\lt \inf[\sigma(\triangle
+V_0)\cap (0, \infty)]$,
$V_1\in C(\mathbf{R}^N)$ and $\lim_{x\to\infty}V_1(x)=0$. A new superquadratic
condition is obtained,
which is weaker than some well known results.


436  Globally Asymptotic Stability of a Delayed IntegroDifferential Equation with Nonlocal Diffusion Weng, Peixuan; Liu, Li
We study a population model with nonlocal diffusion, which
is a delayed integrodifferential equation with double nonlinearity
and two integrable kernels. By comparison method and analytical
technique, we obtain globally asymptotic stability of the zero
solution and the positive equilibrium. The results obtained
reveal that the globally asymptotic stability only depends on
the property of nonlinearity. As application, an example for
a population model with age structure is discussed at the end
of the article.

